Multiple Apple TV Bose on same network

When you say 'it will not allow...' please elaborate.

This could be that the bedroom AppleTV doesn't appear in the list of available AirPlay devices on your phone,

or if could be that you can select the bedroom AppleTV but no audio plays.

or it could be that you can select the bedroom AppleTV, but it gives some kind of error message when you try

All of these have different causes and potential paths to resolution.

At a high level I'd think it's something to do with your network topology, but knowing the symptoms is a necessary first step.

You can use the Amazon Prime server pushed channel and the Apple TV server pushed channel available directly on the Apple TV 3rd generation instead of trying to Airplay.

Beyond that, what exactly happens when you try to Airplay?

Does the TV not appear as an airplay location on the iPhone?

Is the iPhone connected to the same Wi-fi network as the Apple TV in the bedroom?

Is your router separating the networks for 2.4GHz and 5Ghz?

why not just use the prime app on the appletv and skip airplay ?

That generally means something is getting separated.

Check the Wi-Fi networks on each device, and make sure they are named exactly the same.